Find the roots of the quadratic equation `(3x-5)(x+3)=0`.

Answer

To find the roots of the quadratic equation \((3x-5)(x+3)=0\), we will follow these steps:

### Step 1: Set the equation to zero
The equation is already set to zero:
\[ (3x - 5)(x + 3) = 0 \]

### Step 2: Apply the Zero Product Property
According to the Zero Product Property, if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor to zero:
1. \(3x - 5 = 0\)
2. \(x + 3 = 0\)

### Step 3: Solve the first equation
Now, let's solve the first equation:
\[ 3x - 5 = 0 \]
Add 5 to both sides:
\[ 3x = 5 \]
Now, divide both sides by 3:
\[ x = \frac{5}{3} \]

### Step 4: Solve the second equation
Next, we solve the second equation:
\[ x + 3 = 0 \]
Subtract 3 from both sides:
\[ x = -3 \]

### Step 5: State the roots
The roots of the quadratic equation \((3x-5)(x+3)=0\) are:
\[ x = \frac{5}{3} \quad \text{and} \quad x = -3 \]

### Final Answer
The roots are \(x = \frac{5}{3}\) and \(x = -3\).

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